Week 4: You can't prove that I didn't write this in October

This week we talked about transitivity, limits, and structured proofs.

The definition of a limit was a little hard for me to understand. For example, take the function we saw in lecture, f(x) = x^2:

When I had first seen something similar to this in a calculus textbook, it made no sense to me. But in the context of this lecture, one way that I think of it is: "If my enemy chooses any e, then I can choose a d such that for all x-values that differ from 2 by less than d, the corresponding f(x) values will differ from 4 by less than e." So for some function g(x):

From this, I can see how as d gets smaller (x → xo), e can also get smaller (y → yo), so that:

We also started learning about proofs, and looked at some examples for direct proofs of universally quantified implications. I appreciate how rigorous proofs are, and how clearly and throughly one step must lead to the next, so that ultimately P leads to Q, and the implication is undeniably true.

Then we came across the "unexpected hanging paradox", and for a second I felt like I had just unlearned everything from the last twenty minutes!